Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-04-30T23:41:43.537Z Has data issue: false hasContentIssue false
  • English
  • Français

An optimal inspection and replacement policy for a deteriorating system

Published online by Cambridge University Press:  24 August 2016

Masamitsu Ohnishi ,
Hajime Kawai  and
Hisashi Mine
Masamitsu Ohnishi*
Affiliation:
Kyoto University
Hajime Kawai*
Affiliation:
University of Osaka Prefecture
Hisashi Mine*
Affiliation:
Kansai University
*
∗Postal address: Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan.
∗∗Postal address: Department of Business Administration, School of Economics, University of Osaka Prefecture, Osaka 591, Japan.
∗∗∗Postal address: Department of Management Engineering, Faculty of Engineering, Kansai University, Osaka 564, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

Keywords

CONTINUOUS-TIME MARKOVIAN DETERIORATIONEXPECTED TOTAL LONG-RUN AVERAGE COST
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 973 - 988
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Derman, C. (1970) Finite State Markovian Decision Processes. Academic Press, New York.Google Scholar
Drenick, R. F. (1960) Mathematical aspects of the reliability problem. J. SIAM 8, 125–149.Google Scholar
Flehinger, B. J. (1962) A Markovian model for the analysis of the effect of marginal testing on system reliability. Ann. Math. Statist. 33, 754–766.Google Scholar
Kao, E. P. C. (1973) Optimal replacement rules when changes of states are semi-Markovian. Operat. Res. 21, 1231–1249.Google Scholar
Karlin, S. (1968) Total Positivity, Vol. 1. Stanford University Press, Stanford, Ca.Google Scholar
Luss, H. (1976) Maintenance policies when deterioration can be observed by inspections. Operat. Res. 24, 359–366.Google Scholar
Mine, H. and Kawai, H. (1975) An optimal inspection and replacement policy. IEEE Trans. Reliability 24, 305–309.Google Scholar
Mine, H. and Kawai, H. (1982) An optimal inspection and maintenance policy of a deteriorating system. J. Operat. Res. Japan 25, 1–15.Google Scholar
Rosenfield, D. (1976) Markovian deterioration with uncertain information. Operat. Res. 24, 141–155.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar